Compressive Sensing Using Iterative Hard Thresholding with Low Precision Data Representation: Theory and Applications

TL;DR

This paper investigates aggressive data quantization in compressive sensing, providing theoretical guarantees for the normalized IHT algorithm and demonstrating significant speed-ups in radio astronomy and MRI applications with minimal quality loss.

Contribution

It offers a theoretical analysis of low-precision normalized IHT with recovery guarantees and applies this framework to accelerate imaging in astronomy and medical fields.

Findings

Achieved up to 9x speed-up in image recovery

Low-precision data representation maintains recovery quality

Validated on telescope and brain imaging data

Abstract

Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal loss, and the need for careful optimization of the compression ratio. In this work, we focus on a setting where this problem is especially acute: compressive sensing frameworks for interferometry and medical imaging. We ask the following question: can the precision of the data representation be lowered for all inputs, with recovery guarantees and practical performance? Our first contribution is a theoretical analysis of the normalized Iterative Hard Thresholding (IHT) algorithm when all input data, meaning both the measurement matrix and the observation vector are quantized aggressively. We present a variant of low precision normalized {IHT} that, under mild conditions, can still provide recovery guarantees. The second contribution is the application of our quantization framework to radio astronomy and magnetic resonance imaging. We show that lowering the precision of the data can significantly accelerate image recovery. We evaluate our approach on telescope data and samples of brain images using CPU and FPGA implementations achieving up to a 9x speed-up with negligible loss of recovery quality.